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# Title: Leibniz-Handschriften zur Optik und Dioptrik LH 37, 2
# Folio 84v, page id 00068531:0168
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 91r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068531&page=168
# Source image: https://digitale-sammlungen.gwlb.de/content/00068531/jpgs/default/00000168.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 26 lines, status machine
# Lines: 26 recognised, mean confidence 0.91
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Ad quod demonstrandum factum sit hoc scema in quo X,
sit Cenirum Civadli XDB; XD semidiameter. BF
perpindicularis ad DXi DC tangens circulum in B, L.BXG-
ricta ad quam IG et AL popondiculares sunt; AB
parallelae recta DXI. Sijam AD sumatur pro quolibet
radiorum pir aerem transcuntium, et in B in vitrum
circulavis hujus figurae incidentium, calculo jumemiendum
est: prino, punctum illud improduca diametro virsus quod
radius iste rifranus tendit; quod siproceo statuatur
I, inuenenda est longitudo lincae NL. Qua vi jumemratur
sit BX ∞1. BFXX. X 1XZ
AL7y. ABX BI. Pam
porro manifirtum ert triangula ALB, BFX, 1G N, propor
tionalia esse, ac prophrea BF, X, habore eaudem rationem
ad B. N, 1, ut AL, y; ad AB, aut B1, Z; ergo quadatum
supir B2∞ 2y
XF, vudo subvatunquadratum super BF
relinguitur quadvatum supor 1 F ∞ yZ = X X, ergo IF X VyZ - X X
X X
 X
vudo Subtdahatur F N XSi = ZX, vilinguetur X 1XZ∞ V7Z -XX
X X
=V = XX. Povro BXL, 1, est ad BF, X, Vt NI, 2 ad tG∞XZ;
Cum itaque ratio AL ad 1G sit communis monsuva rosractionis
omniumradiorum, et apparet ex secundo capite Dioptrices
pradicsi 8om Dn Cartes; cognita rofractionum orto